The perpetual scourge of EcoGeekiness is obsolescence. We pay good
money for what we see as a good product, and then five years down the
line we’re surrounded by useless junk!

But I can’t help but answer this seemingly straightforward question with several different answers.
First, I’ll actually answer the question:
Yes, you can, but it’s not as simple as curbside pickup. CDs and DVDs
do contain valuable materials (CDRs even sometimes contain gold) and
there are techniques to harvest that material for reuse, but those same
materials make them too complicated for regular recycling centers.
Unfortunately, the materials aren’t expensive enough that someone will
pay for them. To recycle CDs you’ll have to ship them to a special
recycling center. Several are listed at the bottom of this post.